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Kuhn, F. and Moscibroda, T. and Nieberg, T. and Wattenhofer, R. (2005) Local Approximation Schemes for Ad Hoc and Sensor Networks. In: 2005 Joint Workshop on Foundations of Mobile Computing, 02 Sep 2005, Cologne, Germany. pp. 91-106. ACM Press. ISBN 1-59593-092-2
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Official URL: http://doi.acm.org/10.1145/1080810.1080827
We present two local approaches that yield polynomial-time approximation schemes (PTAS) for the Maximum Independent Set and Minimum Dominating Set problem in unit disk graphs. The algorithms run locally in each node and compute a (1+ε)-approximation to the problems at hand for any given ε > 0. The time complexity of both algorithms is O(TMIS + log*! n/εO(1)), where TMIS is the time required to compute a maximal independent set in the graph, and n denotes the number of nodes. We then extend these results to a more general class of graphs in which the maximum number of pair-wise independent nodes in every r-neighborhood is at most polynomial in r. Such graphs of polynomially bounded growth are introduced as a more realistic model for wireless networks and they generalize existing models, such as unit disk graphs or coverage area graphs.
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